1

Chapter 3

AlAs/In0.53Ga0.47As Double Barrier Resonant Tunneling Diodes (DBRTDs)

In this chapter we will briefly describe the operation of DBRTDs and their

potential application at very high frequencies. It will be shown why

AlAs/In0.53Ga0.47As rather than AlAs/GaAs or AlSb/InAs is the material system of

choice for obtaining increased ∆J, the available current density. The effect ofvarying the AlAs/In0.53Ga0.47As DBRTD barrier thickness on the J - V

characteristics will also be discussed.

3.1 Introduction

Electron tunneling through multiple barriers has been studied since the advent of quantum

mechanics. The Kronig-Penny model, published in 1930, describes the coherent interaction of an

electron with a one dimensional periodic potential. An electron experiencing such a periodic

potential can have only certain allowed energy values separated by forbidden energy gaps [1]. Two

decades later, David Bohm in his textbook, "Quantum Theory," solved the double barrier problem in

the WKB approximation and pointed out that resonances in the transmission coefficient occur for

certain incident electron energies [2]. However, it remained a textbook problem until the early

1960's when it was realized that this phenomenon could be observed in a mesoscopic man-made

device. Davis and Hosack in 1963 analyzed the electron transmission coefficient of a thin-film

triode that was modeled as a double barrier with the third contact applied to a layer between the

double barrier layers [ 3]. This structure was the forerunner of the present resonant tunneling

transistor [4]. In an independent effort, Iogansen in the Soviet Union published a paper in 1964

pointing out the possibility of resonant transmission of electrons through double barriers formed

from semiconductor crystals [5]. Then, in the early 1970's, R. Tsu and L. Esaki computed the two-

terminal I - V characteristics of a finite superlattice with the transfer matrix method of Kane. They

showed that resonances are observable not only in the transmission coefficient but also in the I - V

characteristics [6]. They confirmed their calculations in 1974 by demonstrating resonant tunneling

of electrons in MBE grown double barrier structures consisting of a thin GaAs well between

2

AlGaAs barriers [7]. The resonances were observed at liquid nitrogen temperatures as peaks and

inflections in the I - V characteristics at voltages corresponding to the energy of the quasi-bound

states in the quantum well.

However the field lay dormant until 1983 when Sollner et al. demonstrated radio frequency

(RF) detection and mixing at frequencies up to 2.5 THz with Al0.25Ga0.75As/GaAs DBRTDs [8].

Such high frequency operation implied that the intrinsic charge transport mechanism in these

devices was on the order of hundreds of femtoseconds. These results created a surge of interest in

DBRTDs as potential high frequency sources at millimeter and sub-millimeter wavelengths and as

ultra-fast logic elements. DBRTD oscillators soon followed [9] and worldwide efforts to develop

high frequency DBRTDs were initiated. Advances in DBRTDs and quantum-effect devices, in

general, have resulted from improvements in epitaxial growth technology, in particular, MBE and

MOCVD.

The study of the phenomenon of resonant tunneling is now a vast discipline with many sub

fields. The DBRTD has been investigated extensively both as a tool for studying physical processes

in semiconductor heterostructures and for ultra-high speed device applications. From a fundamental

physics aspect, various physical phenomena such as hot-electron transport, localization and quantum

interference effects, scattering at hetero-interfaces, and tunneling through barriers can be studied

with DBRTDs [10]. This work, however, focuses on the application of DBRTDs as high frequency

oscillators. We will begin with a brief review of the physical principles of operation of DBRTDs.

The conduction energy band profile in a AlAs/GaAs DBRTD is shown in Fig. 3.1(a). Due

to the thin GaAs layer, quantum size effects result in the formation of a quasi-bound state at energy

Eo [11]. If the barriers are thin enough, then an electron with this energy can resonantly tunnel from

one electrode through the well to the other electrode. As illustrated in Fig. 3.1(b), as the voltage is

increased, electrons from the degenerately doped emitter electrode tunnel through the quantum well

into an empty state in the collector electrode. As the voltage is increased further, the current

increases until the emitter conduction band edge sweeps past the quasi-bound state. Once the peak

current is reached, applying further voltage will move the emitter conduction band edge above the

quasi-bound state and the current will drop (Fig. 3.1(c)) as the electron transmission through the

quantum well is reduced. This phenomenon gives rise to negative differential resistance (NDR) in

3

the I - V curve as shown in Fig. 3.1(d). The current will eventually rise again with further applied

voltage. The physical mechanisms causing this post-valley current are difficult to represent in the

simple picture of Fig. 3.1 and are related to complex bandstructure effects. This point will be

discussed in further detail later in this chapter.

Assuming that the applied voltage drops uniformly across the quantum well region only

and neglecting any parasitic series resistance, the peak voltage will be equal to 2Eo/q as shown in

Fig. 3.1 (d). This is due to the fact that an applied bias of Eo/q will bring the emitter Fermi level

only half-way up to Eo since the voltage is dropped equally across each barrier. This assumption is

valid only if the heavily doped contact layers are immediately adjacent to the quantum well. In

DBRTD oscillator diodes, however, a significant fraction of the applied voltage is dropped across

the spacer layers outside the quantum well. In fact, in chapter 4, we will see how a judicious choice

of spacer layer profiles can significantly enhance the DBRTD oscillator diode output power.

The salient points of interest in Fig. 3.1 (d) are the peak current density, Jp, the valley

current density, Jv, the peak voltage, Vp, and the valley voltage, Vv. Figures of merit for high speed

DBRTDs are the Jp and peak-to-valley-current ratio (PVCR) and they should be as large as possible.

4

GaA

s

GaA

s

GaA

s

EF EFEO

AlA

s

Voltage

Voltage

DepletionRegion

e-

e-

(a)

(b)

(c)

Voltageq

2Eo

(d)

Cur

rent

Den

sity

Jp

Jv

Vv

Vp

Fig. 3.1 Conduction band-edge profile of DBRTD at (a) equilibrium (b) atresonance (c) off-resonance (d) I - V characteristic showing NDR.Adapted from Sollner et al., Appl. Phys. Lett., vol. 43, No. 6, pp.588-590, 1983.

5

3.2 Self-consistent Schrodinger/Poisson DBRTD Simulation

To accurately calculate the DBRTD I - V characteristics, space charge effects must be

incorporated by self-consistently solving Poisson's equation with the electron concentration

calculated with Schrodinger's equation [12]. We begin by assuming that the DBRTD is described by

the following single particle Hamiltonian [13]

H = − h2

8π 2m *∂ 2

∂z2+ v z( ) (3.1)

where m* is a position independent effective mass, v(z) includes the self-consistent

Hartree potential and any conduction band offsets in the device, and h is Planck's

constant. The simulation domain is discretized in space and the electron

concentration at the grid point j is

n j =4πm * kBT

h2dE

hsL E( )VL

∞∫ ln 1 + e

− E−µL( ) kBT( )ψ L, j E( )ψ L, j* E( )

+ dEhsR E( )VR

∞∫ ln 1 + e

− E−µR( ) kBT( )ψ R, j E( )ψ R, j* E( )

(3.2)

where the subscripts R and L (right and left) on the wave functions ψ denote thecontacts with which the corresponding states are in equilibrium, s and µ are theelectron group velocity and chemical potential respectively, and the subscripts R

and L denote the contacts where they are defined. The complex wave function ψcorresponding to the energy E is obtained by solving the set of difference equations

Hψ j = −1

2m * ∆ Z2

ψ j−1 +1

m * ∆ Z2

+ v j

ψ j −1

2m * ∆ Z2

ψ j+1 = Eψ j (3.3)

6

At each energy E in the domain of integration in Eq. (3.2), the set of equations in

Eq. (3.3) is augmented with quantum transmitting boundary conditions [14]. The

modification of the electrostatic potential due to the electron density computed

above is then calculated by solving Poisson's equation between the two contacts:

d

dzε z( ) d

dz−V z( )( )

= q ND

+ z( ) − n z( )[ ] (3.4)

The Schrödinger and Poisson equations are solved iteratively until self-consistency

is achieved. Finally the current through the device is calculated using the Esaki-

Tsu like expression:

J = qmc

*

2π 2h3dEl∫ dEt∫ T E, Et( ) f L E( )− f R E + qV( )[ ] (3.5)

where El and Et are, respectively, the longitudinal and transverse component of the electron total

energy E; fL(E) and fR(E) are, respectively, the Fermi-Dirac distribution function in the left and

right contacts; V is the bias applied across the structure, mc is the electron effective mass in the

contact; and T(E,Et) is the electron transmission coefficient.

Shown in Fig. 3.2 is a plot of the equilibrium electron transmission coefficient, T(E,Et),

and conduction energy band diagram for a baseline AlAs/In0.53Ga0.47As DBRTD, whose quantum

well consists of a 50Å In0.53Ga0.47As layer sandwiched between 17Å AlAs barriers. Clearly seen

are the extremely sharp resonances of the two peaks, which correspond to the first and second quasi-

bound states. The first quasi-bound state energy, Eo, is 145 meV above the In0.53Ga0.47As

quantum well conduction band edge.

7

[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[

[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[

[[[[[[[[[[[[[[[[[[[[[[

[[[

[[[[[[[[[

[[[

[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[

[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[ [ [ [[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[

[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[

[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 200 400 600 800 1000 1200

1x10-4 1x10-3 1x10-2 1x10-1 1

Ene

rgy

(eV

)

Position (Angstroms)

T*T

Fig. 3.2 Transmission coefficient and conduction band diagram forAlAs/In0.53Ga0.47As DBRTD at equilibrium. Plot provided by K.Gullapalli.

The calculated J - V characteristic of the same structure is shown in Fig. 3.3 with Vp and Jp

equal to 0.8 V and 130 kA/cm2, respectively. The measured J - V characteristic is given in Fig. 4.6

and the measured Vp and Jp are 1.0 V and 95 kA/cm2, respectively. Note that 2Eo/q for this

structure is only 0.29 V. Therefore, a significant fraction of the applied voltage is dropped across

the spacer layers in the downstream depletion region and upstream accumulation region. The

electron effective mass used in the AlAs barrier that provided the closest match to experimental data

was 0.12mo, which is lower than the bulk AlAs Γ-point electron effective mass of 0.15mo. The

calculated peak current density is a strong function of the electron effective mass, which should be

considered a fitting parameter. For example, reducing the AlAs effective mass to 0.08mo results in

a calculated peak current density of 250 kA/cm2, a factor of two greater than the case when mAlAs

equals 0.12mo.

8

1.00.80.60.40.20.00

25

50

75

100

125

150

Voltage (Volts)

Cu

rren

t D

ensi

ty (

kA/s

q.

cm)

Fig. 3.3 Self-consistent Schrodinger/Poisson calculation of J - V characteristic ofAlAs/In0.53Ga0.47As DBRTD. Plot provided by K. Gullapalli.

A further point to be noted is that the PVCR calculated with the self-consistent

Schrodinger-Poisson solver is about 145, which is a factor of fifteen greater than the measured

PVCR. This large disparity is due to the fact that realistic band structure effects (i.e., multiple

valleys, non-parabolicity, multiple bands, etc.) and phonon and impurity scattering have not been

considered. To accurately calculate J - V characterisitcs and incorporate these effects, quantum

kinetic approaches based, for example, on the Lattice Wigner function must be employed [15].

These techniques, however, are in their initial stages of development and extremely computationally

intensive and application to realistic devices is very limited. Although the PVCR can not be

accurately calculated with the self-consistent Schrodinger-Poisson technique, it is nevertheless quite

useful as a device design tool since the peak voltage and peak current density can be calculated quite

accurately and rapidly.

3.3 DBRTDs as high frequency devices

9

The potential for high speed operation of tunneling devices can be seen by representing the

device with the parallel RC equivalent circuit shown in Fig. 3.4.

R = 1/G C

Fig. 3.4 Parallel RC equivalent circuit of intrinsic tunneling diode neglecting anyparasitic series resistance.

If the device length, L, is thin enough and the carrier transport is dominated

by tunneling, it is reasonable to expect an exponential dependence of R on L. The

device's RC time constant, τ, then scales with L as follows

τ = RC = C 1G

α 1L

1

eλ

Lα e

−λ L

L(3.6)

where λ is a proportionality constant relating the conductance to the device length.Thus as L is reduced τ decreases exponentially with a corresponding increase in thefrequency response. In DBRTDs and p-n junction tunnel diodes, L is typically

100Å or less. Consequently, tunneling devices are expected to have very high

frequency response since the conductance is high enough to prevent the shunt

capacitance from dominating the device characteristics until the very highest

frequencies are reached. DBRTDs offer a significant advantage over p-n junction

10

tunnel diodes since much higher conductances and lower capacitances can be

achieved. Furthermore, the p-n junction tunnel diode I - V characteristics are

essentially limited by the material properties, whereas DBRTDs can be engineered

by varying the quantum well dimensions and material properties with MBE.

The high speed properties of DBRTDs have found recent use in switching

and trigger circuits. Ozbay et al. have measured DBRTD switching times as low as

1.7 ps, the fastest switching time reported for any semiconductor device [16]. They

have also demonstrated 110 GHz trigger circuits by monolithically integrating

DBRTDs into coplanar transmission lines [17]. However, the surge of interest in

DBRTDs was originally due to their promise as oscillators and not as logic

elements. The inherent NDR observed in the I - V characteristic and the rapid

tunneling transport mechanism make DBRTDs attractive candidates for high

frequency (greater than 100 GHz) oscillator applications.

A further advantage of DBRTDs over p-n junction tunnel diodes is that the

voltage and current scales are much larger in DBRTDs. Therefore, much larger RF

output powers can be obtained. This can be understood if one considers Fig. 3.5

where the device is biased in the middle of the NDR region and a sinusoidal

voltage is applied to the device. The RF output power density is then, in the low

frequency limit, proportional to the ∆V∆J product. Therefore, to increase the RFoutput power, the ∆V∆J power density product must be maximized. Theoptimization of the ∆V∆J power density product is the subject of the rest of chapter3 and chapter 4.

11

Cur

rent

Den

sity

Voltage

Vosc

∆J

∆V

POUT α ∆V • ∆J

Josc

Fig. 3.5 When DBRTD is biased in the NDR region and a sinusoidal voltage isapplied across the device as shown, the RF output power density isproportional to the ∆V•∆J product.

3.4 AlAs/In0.53Ga0.47As: Material system of choice

To increase the RF output power both ∆V and ∆J must be increased. Wewill see in the next chapter that by adding a moderately thick spacer layer of the

appropriate length, one can increase the ∆V over that of a baseline DBRTD. Toincrease ∆J, one must increase the peak current density as ∆J is given by thefollowing relation

∆J = Jp 1 −1

PVCR

(3.7)

However, in the AlAs/GaAs material system, as one reduces the barrier thickness,

the PVCR suffers and ∆J does not increase as rapidly as one would expect. Forexample, AlAs/GaAs DBRTDs with 14Å (5 monolayer (ML)) AlAs barriers and

50Å (18 ML) GaAs quantum well have peak current densities as high as 250

12

kA/cm2 but the ∆J is 110 kA/cm2 since the PVCR is only 1.8 [18]. The reduction inPVCR can be understood by examining Fig. 3.6 which illustrates the AlAs/GaAs

conduction band structure with the X-point band edge in bold and the Γ-point bandedge in the thin line. For the AlAs/GaAs heterojunction, the ∆EΓΓ and ∆EΓXbarrier heights are 1.05 eV and 0.20 eV, respectively [19]. Also shown is the Γ-Xvalley separation in GaAs, which is approximately 0.48 eV.

Since the ΓGaAs - XAlAs barrier is much lower than the ΓGaAs - ΓAlAs barrier,it is expected that the smaller ∆EΓX barrier height will play a significant role incarrier transport. In fact, it is now well established that the small ∆EΓX barrier

tunneling is a dominant component of the valley current in AlAs/GaAs DBRTDs[20]. The valley current dependence on the ∆EΓX barrier has been confirmed by

many workers through hydrostatic pressure experiments.

∆EΓΓ = 1.05 eV

∆EΓX = 0.2 eV

X

AlAs/GaAs

0.48 eV

Γ

Fig. 3.6 Conduction band edge profile for AlAs/GaAs DBRTDs showing both the∆EΓΓ (1.05 eV) and ∆EΓX (0.20 eV) barrier heights. Also shown is the Γ-X valley separation in GaAs (0.48 eV).

13

These experiments involve measuring the DBRTD J - V characteristics as afunction of hydrostatic pressure. This technique relies on the fact that ∆EΓX barrier

height varies strongly with pressure, decreasing at a rate of 11 meV/kbar, while the∆EΓΓ barrier height is essentially independent of the applied pressure [21]. Using

this approach, Mendez et al. have shown that the resonant tunneling current, which

is the dominant component of the peak current, is determined by the Γ -Γ bandprofile [22]. Their results also indicate that non-resonant tunneling current occursprimarily through the lowest barrier, the ∆EΓX barrier. The valley current due to

this non-resonant or inelastic tunneling current, is composed of phonon-coupled

and impurity-assisted tunneling components [23]. The ratio of the resonant to the

non-resonant tunneling current determines the PVCR and has been shown to

influenced by the AlAs barrier width. Kyono et al. have conducted temperature

dependent I - V measurements on single barrier AlAs/GaAs diodes in which they

varied the barrier width from 14.2Å to 150Å [24]. Their measurements indicate that

elastic tunneling dominates for very thin (14.2Å) AlAs barriers while thermionic

emission is the primary transport mechanism in thick (150Å) AlAs barriers. The

current in the intermediate thickness range, however, appears to consist of both

elastic tunneling and inelastic tunneling components through the Γ GaAs - XAlAsbarrier.

A thorough investigation of the pressure dependence of X-point and Γ-pointrelated tunneling resonances in AlAs/GaAs DBRTDs has recently been conducted

by Austing et al. [25]. They show that for AlAs barriers 30Å and thicker,

hydrostatic pressure reduces the PVCR significantly and with high enough pressure

the NDR completely disappears. The AlAs barrier thicknesses discussed in our

work are thinner (14Å to 20Å) and the current transport mechanism contributing to

the peak current is Γ-point dominated. However, the valley current definitely has astrong X-point related tunneling component. In fact, Cheng et al. reported

improved PVCR in AlAs/GaAs DBRTDs which utilized a four monolayer

Al0.14Ga0.86As "chair" barrier adjacent to one of the AlAs barriers [26]. They

attributed the improved PVCR to a reduction in the resonant tunneling and X-point

14

mediated tunneling components of the valley current. We have also fabricated

AlAs/GaAs DBRTDs with a four monolayer Al0.2Ga0.8As chair barrier adjacent to

one of the AlAs barriers and have achieved a PVCR of 6.3 [27]. This is the highest

reported PVCR at room temperature for AlGaAs/GaAs DBRTDs and the reader is

referred to Alwin Tsao's Ph.D. dissertation for further details [28]. Although, the

chair barrier approach does result in a higher PVCR, it does so at the expense of

reduced Jp and ∆J, since the chair barrier results in an effectively thicker barrier.Another approach to increasing the Jp and PVCR in AlAs/GaAs DBRTDs has been

to insert a pseudomorphic In0.15Ga0.85As "pre-well" adjacent to one of the AlAs

barriers, resulting in a PVCR of 7.2 at room temperature but with a Jp of only 10

kA/cm2 [29]. Recently, Yang et al. demonstrated AlAs/GaAs DBRTDs with a

linearly graded AlGaAs layer adjacent to the AlAs barrier [30]. The purpose of this

graded layer was to reduce the hump in the conduction band that is caused by space

charge effects in the spacer layers used in conventional structures. By

incorporating this graded AlGaAs layer, they achieved a Jp of 170 kA/cm2 with a

PVCR of 3.2 (∆J = 170 kA/cm2). Although this is quite an impressive result forGaAs based DBRTDs, higher performance can be achieved with

AlAs/In0.53Ga0.47As DBRTDs as will be shown later. Furthermore, reproducible

MBE growth of the graded AlGaAs layer required in such a structure is difficult

and variations in the grading will have significant impact on the J - V

characteristics.

The above discussion illustrates the importance of X-point related transport

in AlAs/GaAs DBRTDs and suggests that higher performance (higher Jp without

sacrificing PVCR) can be achieved if the ∆EΓX barrier height can be increased.

Such an increase is possible if the quantum well material system is changed to the

AlAs/In0.53Ga0.47As material system. The conduction band edge for the

AlAs/In0.53Ga0.47As system is shown in Fig. 3.7 where the ∆EΓΓ and ∆EΓX barrierheights are 1.2 eV and 0.65 eV, respectively [27]. The Γ-X valley separation inIn0.53Ga0.47As, approximately 1.05 eV, is much higher than in GaAs [

31].

15

∆EΓΓ = 1.20 eV

∆EΓX = 0.65 eV

X

AlAs/In0.53Ga0.47As

Γ

1.05 eV

Fig. 3.7 Conduction band edge profile for AlAs/In0.53Ga0.47As DBRTDs showing

both the ∆EΓΓ (1.2 eV) and ∆EΓX (0.65 eV) barrier heights. Also shownis the Γ-X valley separation in GaAs (1.05 eV).

Comparing the two conduction band profiles in Figs. 3.6 and 3.7, one seesthat while the ∆EΓΓ barrier heights are similar, the ∆EΓX barrier height is muchhigher in the AlAs/In0.53Ga0.47As material system. Therefore, this material system

should be superior to the AlAs/GaAs material system since the parasitic Γ-Xmediated transport will be reduced.

Inata et al. were the first to study AlAs/In0.53Ga0.47As DBRTDs and they

observed that for a given Jp, a higher PVCR could be achieved with

AlAs/In0.53Ga0.47As DBRTDs than with AlAs/GaAs DBRTDs [32]. Interest in this

material system grew when Broekaert et al. reported AlAs/In0.53Ga0.47As/InAs

DBRTDs with PVCRs as high as 30 at room temperature [33]. The AlAs barriers in

these devices were ten monolayers thick and Jp was quite low, about 5 kA/cm2.

16

Nevertheless, this result generated interest since, at the time, that was the highest

PVCR ever reported for DBRTDs. Then, Broekaert et al. reported

AlAs/In0.53Ga0.47As DBRTDs with peak current densities as high as 460 kA/cm2

with a PVCR of 4 [34]. This results in a ∆J of 345 kA/cm2, which is the highest ∆Jreported in any material system. To achieve such high Jp, extremely thin (four ML)

AlAs barriers and a 16 ML In0.53Ga0.47As quantum well were employed. As a

point of comparison, no AlAs/GaAs DBRTDs have been even reported with such

high Jp. The above discussion makes clear that the AlAs/In0.53Ga0.47As material

system is the preferred system for high speed oscillator applications since both high

Jp and PVCR DBRTDs can be fabricated.

3.5 AlAs/In0.53Ga0.47As DBRTDs: barrier thickness dependence

This section discusses the barrier thickness dependence of the J - V

characteristics of thin barrier AlAs/In0.53Ga0.47As DBRTDs. AlAs/In0.53Ga0.47As

DBRTDs with barrier thicknesses of 5, 6, and 7 monolayers were fabricated and

tested. The layer schematic of the devices is shown in Fig. 3.8. Sulfur doped (n =

3 x 1018 c m-3) liquid encapsulated Czochralski grown InP substrates from

Sumitomo Chemical were used. Heavily doped (n = 2.2 x 1019 cm-3), 2000Å thick

top and bottom buffer In0.53Ga0.47As layers were employed as contact cladding

layers. The quantum well is sandwiched between a three-step dopant transition

region consisting of 100Å (n = 6.0 x 1017 cm-3) In0.53Ga0.47As, 100Å (n = 4.3 x

1016 cm-3) In0.53Ga0.47As, and finally 50Å of nominally undoped ( n = 5 x 1015 cm-

3) In0.53Ga0.47As adjacent to the AlAs barrier. The quantum well consists of a 50Å

nominally undoped In0.53Ga0.47As quantum well and pseudomorphic AlAs barriers.

No growth interruption at the hetero-interfaces was used. The device fabrication

process and electrical test procedure are given in Appendix 1.

17

n+ InP substrate

2000Å

100Å

100Å

50Å

L

50Å

L

50Å

100Å

100Å

2000Å

2.2 x 1019 cm-3

6.0 x 1017 cm-3

4.3 x 1016 cm-3

4.3 x 1016 cm-3

6.0 x 1017 cm-3

2.2 x 1019 cm-3

Undoped

Undoped

Undoped

Undoped

Undoped

InGaAs

InGaAs

InGaAs

InGaAs

InGaAs

InGaAs

InGaAs

InGaAs

InGaAs

AlAs

AlAs

Fig. 3.8 Layer schematic of AlAs/In0.53Ga0.47As DBRTDs to study the barrierthickness dependence on the J - V characteristics. The quantum wellconsists of a 50Å In0.53Ga0.47As layer sandwiched betweenpseudomorphic AlAs layers of thickness L. Three devices with L = 5, 6,and 7 ML barriers were studied.

18

Shown in Fig. 3.9 are measured J - V characteristics of the three devices.

One can see the dramatic effect that the barrier thickness has on the J - V

characteristics. Decreasing the barrier thickness by one monolayer approximately

doubles the peak current density.

2.01.51.00.50.0-0.5-1.0-1.5-2.0-200

-150

-100

-50

0

50

100

150

200

Voltage (Volts)

Cu

rren

t D

ensi

ty (

kA/s

q.

cm)

L = 5 ML

L = 6 ML

L = 7 ML

Fig. 3.10 Measured J - V characteristics of AlAs/In0.53Ga0.47As DBRTDs withAlAs barrier thicknesses of 5, 6, and 7 ML. The voltage across the 5 MLAlAs barrier DBRTD is corrected for the ohmic contact resistance (pc =10-6 ohm-cm2) since the very high peak current density (Jp ~ 165 kA/cm2)magnifies the ohmic contact resistance effect. This correction results in areduction of Vp of roughly 0.16 V and a corresponding increase in ∆V.Decreasing the barrier thickness by one monolayer increases the currentdensity by roughly 100%.

19

Shown in Table 3.1 are values for the device parameters of interest for the

devices shown in Fig. 3.9. These devices also show an asymmetry in the J - V

characteristics similar to that seen in AlAs/GaAs DBRTDs. Namely, one observes

a higher Jp and lower PVCR for forward bias (electron injection from the

substrate), whereas for reverse bias, the PVCR is higher and the Jp is lower. The

quantum well injection conductance (to be discussed in Chapter 4), extracted from

the J - V characteristics, for the L= 5, 6, and 7 ML samples are - 1.3, -0.5, and -0.3

(ohm - cm)-1, respectively.

Device

Parameter

L=5ML

For.

Bias

Rev.

Bias

L=6 ML

For.

Bias

Rev.

Bias

L=7 ML

For.

Bias

Rev.

Bias

Jp (kA/cm2) 167 166 82 78 35 35

∆J (kA/cm2) 146 148 74 72 32 33PVCR 7.8 9.2 10.1 13 11.4 14.1

Vp 0.92 0.88 0.91 0.76 0.86 0.75

∆V 0.36 0.27 0.4 0.35 0.39 0.33

Table 3.1 Typical device parameter values for AlAs/In0.53Ga0.47As DBRTDs with50Å In0.53Ga0.47As quantum well and barrier thickness of 5, 6, and 7ML.

The peak and valley current density as a function of barrier thickness are

plotted in a semi-log plot in Fig. 3.10. This figure clearly shows the exponential

dependence on barrier thickness that one would expect from Eq. 3.6 where the

conductance is exponentially dependent on the barrier thickness.

20

8765410 0

10 1

10 2

10 3

AlAs Barrier Thickness (monolayers)

Cu

rren

t D

ensi

ty (

kA/s

q.

cm)

J p

J v

Fig. 3.10 Semi-log plot of Jp and Jv as a function of AlAs barrier thickness. Thecharacteristics show the expected exponential dependence on the barrierthickness. The error bars denote a 10% uncertainty in device areameasurement.

This exponential dependence has also been observed by Broekaert et al. [35]

and Chow et al. [36]. If we model the exponential dependence of the peak current

density as

Jp α exp −LBλ

(3.8)

where LB is the barrier thickness in ML and λ is a characteristic length, we find thatλ = 1.3 ML. This indicates that a variation in the barrier thickness on the order of a

21

one monolayer will result in the current density changing by a factor of two.

Therefore, very tight control of the layer thicknesses is required and the techniques

to achieve this level of control have been discussed in the previous chapter.

3.6 Comparison of Material Systems

For DBRTDs to generate useful amounts of output power at very high

frequencies, the ∆J of the device should be as large as possible so as to maximizethe ∆V∆J power density product. We have implied that the AlAs/In0.53Ga0.47Asmaterial system is the system of choice for obtaining this increased ∆J. This wasbased on the observation that for a given Jp, much higher PVCR are obtained in the

AlAs/In0.53Ga0.47As system than in the AlAs/GaAs system. The improved

performance was attributed to the higher ∆EΓX barrier height available with theAlAs/In0.53Ga0.47As system.

One question to be asked is whether the additional effort required to

fabricate AlAs/In0.53Ga0.47As devices is warranted. Furthermore, are there other

material systems that provide performance better or equal to that of the

AlAs/In0.53Ga0.47As system? To answer these questions, we plot ∆J versus Jp at300K in Fig. 3.11 for DBRTDs fabricated in three material systems: AlAs/GaAs,

AlAs/In0.53Ga0.47As, and AlSb/InAs. The AlAs/GaAs data was obtained from

[27],[17], and [29]. The AlAs/In0.53Ga0.47As data was from [32], [33], [34], [37],

and from devices presented in this work. The AlSb/InAs data was obtained from

Soderstrom et al. [38]. The AlSb/InAs system has been suggested as an alternative

to the AlAs/GaAs and AlAs/In0.53Ga0.47As system due to the very high conduction

band offsets available: 1.8 eV for Γ-Γ barrier height and 1.35 eV for the Γ-Xbarrier (InAs Γ-point to AlSb X-point) [39]. This is expected to reduce X-pointmediated tunneling currents and consequently increase the PVCR.

22

100080060040020000

100

200

300

400

500AlAs/GaAsAlAs/InGaAsAlSb/InAs

Peak Current Density (kA/sq. cm)

Del

ta J

(kA

/sq.

cm

)

Fig. 3.11 Comparison of measured ∆J vs Jp at 300K obtained with DBRTDs in theAlAs/GaAs, AlAs/In0.53Ga0.47As , and AlSb/InAs material systems.

Examining Fig. 3.11 we see that for small Jp (less than 50 kA/cm2) all the

points fall on top of each other and there is no significant difference in performance

between the material systems. But as Jp is increased one begins to notice the

performance difference between the material systems. The AlAs/GaAs devices

achieve a maximum ∆J of approximately 130 kA/cm2 at a Jp of 200 kA/cm2.Further increase in Jp results in reduced ∆J since the PVCR begins to drop. TheAlSb/InAs and the AlAs/In0.53Ga0.47As DBRTDs offer a substantial performance

advantage over AlAs/GaAs based devices with ∆J's on the order of several hundredkA/cm2. At a record high Jp of 800 kA/cm2 (achieved with 3 ML AlAs barriers)

the ∆J of the AlAs/In0.53Ga0.47As DBRTDs is essentially zero. This is due to the

23

fact that as the barrier thickness is reduced, the transmission coefficient changes to

that of a single barrier with the consequent loss of NDR. Therefore, ∆J will drop asthe PVCR reduces (see Eq. 3.7). Nevertheless, it is apparent from Fig. 3.11 that the

AlAs/In0.53Ga0.47As devices are superior to the AlSb/InAs devices since they offer

higher ∆J's at very high Jp.

Returning to the questions posed at the beginning of this section, it is quite

clear that the extra effort required for fabricating AlAs/In0.53Ga0.47As devices is

well worth the effort for very high frequency applications where large ∆J isessential. Furthermore, from a device application perspective, AlSb/InAs DBRTDs

may suffer from impact ionization events occurring in the very narrow band gap

InAs (Eg @ 300K = 0.35 eV [40]). This is particularly true for high current density

DBRTDs where electric fields on the order of several hundred kV/cm are

encountered. This will be discussed further in chapters 4 and 5.

3.7 Summary

We have briefly described the operation of DBRTDs and their potential

high speed applications. It was seen that increasing the ∆V∆J product will increasethe DBRTD RF output power. The effect of varying the AlAs/In0.53Ga0.47As.

DBRTD barrier thickness on the J - V characteristics was investigated. Precise

control of layer thicknesses in DBRTDs is essential; since, changing the barrier

thickness by one monolayer results in a factor of two change in the peak current

density. We have also explained why AlAs/In0.53Ga0.47As rather than AlAs/GaAs

or AlSb/InAs is the material system of choice for obtaining increased ∆J, theavailable current density.

24

References

1 R. de L. Kronig and W. G. Penney, " Quantum Mechanics of Electrons in Crystal

Lattices," Proceedings of the Royal Society, A130, p. 499, 1930.

2 David Bohm, " Quantum Theory," Dover Books, New York, 1951.

3 R. H. Davis and H. H. Hosack, " Double Barrier in Thin-Film Triodes," Journal

of Applied Physics, vol. 34, No.4, pp.864-866, 1963.

4 F. Capasso and R. A. Kiehl, " Resonant Tunneling Transistor with Quantum Well

Base and High Energy Injection: A New Differential Resistance Device," J.

Appl. Phys., vol. 58, p. 1366, 1985.

5 L. V. Iogansen, " The possibility of resonance transmission of electrons in

crystals through a system of barriers," Soviet Physics JETP, vol. 18, No. 1,

pp.146-150, 1964.

6 R. Tsu and L. Esaki, " Tunneling in a finite superlattice," Appl. Phys. Lett., vol.

22, No. 11, pp.562-564, 1973.

7 L. L. Chang, L. Esaki, and R. Tsu, " Resonant tunneling in semiconductor double

barriers," Appl. Phys. Lett., vol. 24, No. 12, pp.593-595, 1974.

8 T. C. L. G. Sollner, W. D. Goodhue, P. E. Tannenwald, C. D. Parker, and D. D.

Peck, " Resonant tunneling through quantum wells at frequencies up to 2.5 THz,"

Appl. Phys. Lett., vol. 43, No. 6, pp.588-590, 1983.

9 T. C. L. G. Sollner, P. E. Tannenwald, D. D. Peck, and W. D. Goodhue, "

Quantum Well Oscillators," Appl. Phys. Lett., vol. 45, No. 12, pp.1319-1321,

1984.

25

10 L. L. Chang, E. E. Mendez, and C. Tejedor, Eds., " Resonant Tunneling in

Semiconductors: Physics and Applications," Plenum Press, New York, 1991.

11 Raymond Dingle, " Confined carrier quantum states in ultrathin semiconductor

heterostructures," Festkorperprobleme XV, 1975.

12 M. Cahay, M. McLennan, S. Datta, and M. S. Lundstrom, " Importance of

space-charge effects in resonant tunneling devices," Appl. Phys. Lett., vol. 50,

No. 10, pp.612-614, 1987.

13 Kiran Kumar Gullapalli, Ph.D. Dissertation, May 1994.

14 C. S. Lent and D. J. Kirkner, " The quantum transmitting boundary method," J.

Appl Phys., vol. 67, No. 10, 1990.

15 D. R. Miller, K. K. Gullapalli, V. K. Reddy, and D. P. Neikirk, " Simulation of

Electron Transport in Quantum Well Devices," Proc. of the Third International

Symposium on Space Terahertz Technology, March 24-26, pp.560-574, 1992.

16 E. Ozbay, David. M. Bloom, D. H. Chow, and J. N. Schulman, " 1.7 ps,

Microwave, Integrated-Circuit-Compatible InAs/AlSb Resonant Tunneling

Diodes," IEEE Electron Device Lett., vol. 14, No. 8, pp.400-402, 1993.

17 E. Ozbay and David M. Bloom, " 110-GHz Monolithic Resonant-Tunneling-

Diode Trigger Circuit," IEEE Electron Device Lett., vol. 12, No. 9, pp.480-482,

1991.

18 E. Wolak, E. Ozbay, B. G. Park, S. K. Diamond, D. M. Bloom, and J. S. Harris,

" The design of GaAs/AlAs resonant tunneling diodes with peak current

26

densities over 2 x 105 A/cm2," J. Appl. Phys., vol. 69, No. 5, pp.3345-3350,

1991.

19 Sadao Adachi, " GaAs, AlAs, AlxGa1-xAs: Material parameters for use in

research and device applications," J. Appl. Phys., vol. 58, No. 3, pp.R1-R29,

1985.

20 L. L. Chang, E E. Mendez, and C. Tejedor, eds., " Resonant Tunneling in

Semiconductors: Physics and Applications," Plenum Press, New York, 1991.

21 R. Pritchard, P. C. Klipstein, N. R. Couch, T. M. Kerr, J. S. Roberts, P. Mistry,

B. Soylu, and W. M. Stobbs, " High-pressure studies of resonant tunneling in a

graded parameter superlattice and in double barrier structures of GaAs/AlAs,"

Semiconductor Science and Technology, vol. 4, pp.754-764, 1989.

22 E. E. Mendez, E. Cajella, and W. I. Wang, " Tunneling through indirect-gap

semiconductor barriers," Phys. Rev. B, vol. 34, No. 8, pp.6026-6029, 1986.

23 E. E. Mendez, E. Cajella, and W. I. Wang, " Inelastic tunneling in AlAs/GaAs

heterostructures," Appl. Phys. Lett., vol. 53, No. 11, pp.977-979, 1988.

24 C. Kyono, V. P. Kesan, D. P. Neikirk, C. M. Maziar, and B. G. Streetman, "

Dependence of apparent barrier height on barrier thickness for perpendicular

transport in AlAs/GaAs single-barrier structures grown by molecular beam

epitaxy," Appl. Phys. Lett., vol. 54, No. 6, pp.549-551, 1989.

25 D. G. Austing, P. C. Klipstein, A. W. Higgs, H. J. Hutchinson, G. W. Smith, J.

S. Roberts, and G. Hill," X- and Γ- related tunneling resonances in GaAs/AlAsdouble-barrier structures at high pressure," Phys. Rev. B, vol. 47, No. 3,

pp.1419-1433, 1993.

27

26 P. Cheng and J. S. Harris, " Improved design of AlAs/GaAs resonant tunneling

diodes," Appl. Phys. Lett., vol. 56, No. 17, pp.1676-1678, 1990.

27 V. K. Reddy, A. J. Tsao, and D. P. Neikirk, " High peak-to-valley current ratio

AlGaAs/AlAs/GaAs double barrier resonant tunneling diodes," Electronics

Lett., vol. 26, No. 21, pp.1742-1744, 1990.

28 A. J. Tsao, " Molecular beam epitaxial growth and fabrication of microwave and

photonic devices for hybrid integration on alternative substrates, Ph.D.

Dissertation, The University of Texas at Austin, 1993.

29 H. Brugger, U. Meiners, C. Wolk, R. Deufel, A. Marten, M. Rossmanith, K. v.

Klitzing, and R. Sauer, " Pseudomorphic two-dimensional electron-gas-emitter

resonant tunneling devices," Microelectronic Engineering, vol. 15, pp.663-666,

1991.

30 L. Yang, D. E. Mars, and M. R. T. Tan, " Effect of electron launcher structures

on AlAs/GaAs double barrier resonant tunneling diodes," J. Appl. Phys., vol.

73, No. 5, pp.2540-2542, 1993.

31 Massimo V. Fischetti, " Monte Carlo simulation of transport in technologically

significant semiconductors of the diamond and zinc-blende structures - Part I:

Homogeneous transport," IEEE Trans. on Electron Devices, vol. 38, No. 3,

pp.634-649, 1991.

32 T. Inata, S. Muto, Y. Nakata, S.Sasa, T. Fujii, and S. Hiyamizu, " A

pseudomorphic In0.53Ga0.47As/AlAs resonant tunneling barrier with a peak-

to-valley current ratio of 14 at room temperature," Japanese Journal of

Applied Phys., vol. 26, No. 8, pp.L1332-L1334, 1987.

28

33 T. P. E. Broekaert, W. Lee, and C. G. Fonstad, " Pseudomorphic

In0.53Ga0.47As/AlAs/InAs resonant tunneling diodes with peak-to-valley

current ratios of 30 at room temperature," Appl. Phys. Lett., vol. 53, No. 16,

pp.1545-1547, 1988.

34 T. P. E. Broekaert and C. G. Fonstad, " In0.53Ga0.47As/AlAs resonant tunneling

diodes with peak current densities in excess of 450 kA/cm2," J. Appl. Phys., vol.

68, No. 8, pp.4310-4312, 1990.

35 T. P. E. Broekaert and C. G. Fonstad, " Extremely high current density, low peak

voltage, pseudomorphic In0.53Ga0.47As/AlAs/InAs Resonant tunneling diodes,"

1989 IEDM Technical Digest, pp.559-562, 1989.

36 D. H. Chow, J. N. Schulman, E. Ozbay, and D. M. Bloom, " Investigation of

In0.53Ga0.47As/AlAs/ resonant tunneling diodes for high speed switching," Appl.

Phys. Lett., vol. 61, No. 14, pp. 1685-1687, 1992.

37 E. R. Brown, C. D. Parker, A. R. Calawa, M. J. Manfra, T. C. L G. Sollner, C. L.

Chen, S. W. Pang, and K. M. Molvar, " High-speed resonant-tunneling diodes

made from the In0.53Ga0.47As/AlAs material system,: Proc. on High-Speed

Electronics and Device Scaling, SPIE vol. 1288, pp. 122-135, 1990.

38 J. R. Soderstrom, E. R. Brown, C. D. Parker, L. J. Mahoney, and T. C. McGill, "

Growth and characterization of high current density, high-speed InAs/AlSb

resonant tunneling diodes," Appl. Phys. lett., vol. 58, No. 3, pp.275-277, 1991.

39 J. R. Soderstrom, D. H. Chow, and T. C. McGill, " InAs/AlSb Double-Barrier

Structure with Large Peak-to-Valley Current Ratio: A Candidate for High-

Frequency Microwave Devices," IEEE Electron Device Lett., vol. 11, No. 1, pp.27-

29

29, 1990.

40 A. Cappy, B. Carnez, R. Fauquembergues, G. Salmer, and E. Constant, "

Comparative Potential Performance of Si, GaAs, GaInAs, InAs Submicrometer-

Gate FET's," IEEE Trans. on Electron Devices, vol. 27, No. 11, pp.2158-2160,

1980.